Figure 9: The calculated real and imaginary parts of the dielectric function for LiBH4
In figure (9) blue line indicates the real part, while red line shows imaginary part of dielectric function. The static value of the real part of the dielectric function at zero frequency is found to be 2.25. It extends slightly along the frequency axis upto 5 eV, however, beyond this frequency, its value ascends at the higher frequency and gains maximum value of 5.6. Nevertheless, on increasing the frequency above 7.5 eV, \(\varepsilon_{1}\) descends to zero at 9 eV, it further extends towards its negative values and gains the value of -2 at 10.5 eV frequency. On escalation of the frequency range above 10.5 eV, real part of dielectric function regains its value. After crossing the frequency axis at 14 eV, it extends with positive values but almost parallel to the frequency axis. Moreover, as revealed from figure (9),\(\varepsilon_{2}\) the imaginary value of the dielectric function remains zero upto an energy (frequency) approximately equal to the energy band of the studied material. However, beyond ⁓ 6.88 eV frequencies, the value of \(\varepsilon_{2}\) is noticed to be increased sharply and attains maximum value (5.7) at 8.7 eV frequency. Unfortunately, after that frequency the values of imaginary constant started to decrease and becomes zero at 13 eV frequency.
Refractive index and extinction coefficient
A dimensionless parameter, the refractive index, is in fact a ratio amid velocity of light in a vacuum to the velocity of light passing through the materials. The refractive index, n and dielectric functions (\(\varepsilon_{1}\), \(\varepsilon_{2}\)) are interlinked through the following relations [40]:
\(\varepsilon_{1}=n^{2}-k^{2}\)(3)\(\backslash n\varepsilon_{2}=2nk\) (4)
Where \(k\) defines the extinction coefficient. Figure 10 displays the material’s response associated with refractive index and its imaginary part, i.e., extinction coefficient. The static value of the refractive index n (0) is noted to be 1.5, which however remains unchanged with increasing frequency till 5 eV. Nonetheless, its value grows gradually beyond 5 eV and attains sharp peak at 7.5 eV frequency. Afterwards, the sharp decrease in value of the refractive index has been noticed upto 12.5 eV, which re-escalates at further higher frequency. It has been noticed that refractive index and extinction coefficient both have shown similar pattern as that of the real and imaginary components of the dielectric function. Likewise \(\varepsilon_{2}\), value of the extinction coefficient remains zero equal to the energy band gap of the considered compound, which is the characteristic of the semiconducting materials [44].